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To attack the P = NP question, the concept of NP-completeness is very useful. NP-complete problems are problems that any other NP problem is reducible to in polynomial time and whose solution is still verifiable in polynomial time. That is, any NP problem can be transformed into any NP-complete problem. Informally, an NP-complete problem is an ...
An nth busy beaver, BB-n or simply "busy beaver" is a Turing machine that wins the n -state busy beaver game. [ 5 ] Depending on definition, it either attains the highest score, or runs for the longest time, among all other possible n -state competing Turing machines.
e. In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine.
NEXPTIME. In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using time . In terms of NTIME, Alternatively, NEXPTIME can be defined using deterministic Turing machines as verifiers. A language L is in NEXPTIME if and ...
An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
In computational complexity theory, a complexity classis a setof computational problems"of related resource-based complexity".[1] The two most commonly analyzed resources are timeand memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like timeor memory.
Some machines have additional working tapes, including the Turing machine, linear bounded automaton, and log-space transducer. Transition function. Deterministic: For a given current state and an input symbol, if an automaton can only jump to one and only one state then it is a deterministic automaton.
Class of computational decision problems for which any given yes -solution can be verified as a solution in polynomial time by a deterministic Turing machine (or solvable by a non-deterministic Turing machine in polynomial time). NP-hard. Class of problems which are at least as hard as the hardest problems in NP.